Confidence intervals for the excess risk in case-control studies

Kaufman et al. compute the 'excess risk' of a disease in the presence of an exposure as the product of the incidence rate of the disease in the source population, the complement of the aetiologic fraction and the relative risk minus one. Methods for calculating confidence intervals for this quantity are derived when (as in case-control studies) the relative risk is estimated by the odds ratio, firstly from multiple logistic regression analysis and secondly without adjustment for covariates. For the latter an innovative approach based on confidence bounds for the two exposure parameters is suggested. The performance of these systems of confidence intervals is assessed by simulation for the former and by exact enumeration of the distributions involved in the latter. Illustrative examples from a study of agranulocytosis and indomethacin are presented.